Mr Harrison, Stab ility of the Steady Motion of viscous liquid 455 



On the Stability of the Steady Motion of viscous liquid contained 

 between two rotating coaxal circular cylinders. By W. J. Harrison, 

 M.A., Fellow of Clare College, Cambridge. 



[Received 29 August 192L] 



In the previous paper* on this subject an error has been made 

 which invalidates the results given in Part I. The solution given in 

 equation (26) satisfies equation (25), but is not sufficiently general 

 to provide a solution of the problem, as it makes two values of m 

 identical. This error has been pointed out by Prof, W. M^F. Orr. 

 Between equations (4) and (12) there are also various errors and 

 misprints which are misleading, although they do not affect the 

 subsequent work. A brief statement of these and a sUght modifica- 

 tion of the method of obtaining equation (17) will be given first. 



The equation following (4) is correct. Integrating the last three 

 integrals by parts we obtain the equation preceding (5), except 

 that the final expression in it should be written 



rr du fdu dv\ dvl , 



- J p dx + ^- V8^ + ax j + ^- dyj ^"- 



Equation (5) is correct after making the same alteration. Equations 

 (6) should be written 



:Pxa. = - i? - 1/^ div g + 2/A ^ , etc., 

 /dv du\ 



In equation (7), {^ + ^j should be replaced by (9^ + 9^)' ^^^ 



(8) should be written p' = p + ^JJ- div q. 



The equation giving the critical value of /x for a given disturb- 

 ance is obtained by equating the left-hand side of equation (7) to 

 zero. Varying u, v, p, in this equation, putting hfx = 0, and inte- 

 grating by parts where necessary, we obtain equations determining 

 a state of disturbed motion such that the relative kinetic energy 

 is stationary, ju being at the same time stationary and a maximum. 

 After performing these operations the fluid is treated as incom- 

 pressible. 



Thus we arrive at equations determining the mode of disturb- 

 ance which is most likely to cause the steady motion to change to 

 turbulent motion. Hence for all greater values of ix than that which 

 * Tamaki and Harrison, Trans. Camb. Phil. Soc, vol. xxii, No. 22. 



